The most common and most likely answer to this crossword clue is the 13 letter word PRETERNATURAL
I've seen this crossword clue in The Daily Telegraph
P
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More clues leading to the result PRETERNATURAL
Buddy explains!

The straight part
We know that "Extraordinary" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case extraordinary = preternatural.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does PRETERNATURAL mean?
PRETERNATURAL adjective- Beyond or not conforming to what is natural or according to the regular course of things; strange.
- Having an existence outside of the natural world.